Cougar Software, a fast-growing clothier, just paid a dividend of $1.64. Analysts project annual dividend growth to be 20% for the next 4 years, and then 5% thereafter. If investors’ required rate of return is 8%, what should the price of the stock be? Round to the nearest cent. Do not include the dollar sign in your answer. (i. e. If your answer were $1.23, then type 1.23 without a $ sign)

As per question dividend growth rate would 20% in year 1-4 and 5% in year 5 and thereafter.

Now, D1 = 1.64(1.20) = $1.968

 D2 = $1.968(1.20) = $2.362

D3 = $2.362(1.20) = $2.834

D4 = $2.834(1.20) = $3.401 and,

D5 = $3.401(1.05)= $3.571

Now, here we can calculate P4 with the help of above D5:

P4 = D5 / r-g = $3.571 /(0.08-0.05) = $119.033

so, P4 = $119.033

Thus, Price of stock (P0) = Present value of all future benefits

P0 = Present value of D1, D2, D3, D4 and P4

  = $1.968/1.08 + 2.362/(1.08)2 + 2.834(1.08)3 + 3.401(1.08)4 + 119.033(1.08)4

  = $ 96.0896

Thus, price of stock = 96.1 (rounded to the nearest cent)

96.08

Explanation:

First, we determine the Dividend for the 4 years.

The Just paid dividend = $1.64

Dividend Growth Rate = 20%

D1= P0(1+r)

Dividend for Year 1 (D1) = 1.64 (1.2) = $1.968

Dividend for Year 2 (D2) = 1.968(1.2) = $2.3616

Dividend for Year 3 (D3) = 2.3616 (1.2) = $2.8339

Dividend for Year 4 (D4) = 2.8339 (1.2) = $3.4007

Step 2: We determine the value after the 4th year based on the following formula

(D4 x Growth rate)/ (Required rate of retuurn - Growth Rate)

= ($3.4007 x 1.05)/ (0.08-0.05)

= 3.570735/0.03

= $119.0245‬

Step 3: We determine the current price as follows

Future Dividends x Present value of the Discounting Factor

The Present value of discounting factor will be based on (1+required rate of return)∧n

Present Value = (1.968/1.08)+(2.3616/1.08)^2 +(2.8339/1.08)^3 + (3.4007/1.08)^4+ ($119.025/1.08)^4

= 96.08